If you consider staying the first night in Würzburg then it is an easy train ride to Rothenburg ob der Tauber, but I don't know if you can get a car there.
I think that 3 nights there is a lot. It is really quite a small place and while interesting it is self contained. There are other villages and towns around but Iphofen (my favourite - search on here for various reviews, it isn't in Rick's book) is east and Dinkelsbühl is south (maybe see it on the way by. The storks on the roof may be gone by then - they raise their young every year, and the TI has a video screen if you can't see them - but they were there when we passed through in early July this year).
Due south of RodT at the other end of the "Romantic Road" (think King Ludwig and romantic era music, not lovie dovie romantic) is Füssen. Very easy to reach on either the B road or the parallel autobahn. Then Salzburg (via Munich) on the way to Hallstatt (it is a long way to come back to, do it as you pass - unless you want the Fern Pass and after doing it a few times nobody does, ihmo) but there's always a first time and you might like Oberammergau. Skip Reutte. One night in Füssen should be enough, maybe 2, but it really is a one attraction kind of place, especially with the influx of the tour buses. If you hadn't had the car I would have suggested train to Munich and enjoy a little biergarten action before Austria. Salzburg again very easy by train from Munich, but if you have the car perhaps you can park under the mountain or at a hotel on Moostrasse. Very very expensive parking in Salzburg.
Hallstatt to Castelrotto (suggest Ortesei instead if you want mountains and hiking) then down to Lake Como. If you can tell us what sort of thing you'd like to achieve on Lake Como we may be able to help you choose a village or town. Parking difficult and expensive on Como unless you know where to go, and you can't see the lake or the houses from the road.
Then to Milan.
my 2 eurocents, for what they are worth